<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
 <head>
  <title>chpgvd.f</title>
 <meta name="generator" content="emacs 21.3.1; htmlfontify 0.20">
<style type="text/css"><!-- 
body { background: rgb(255, 255, 255);  color: rgb(0, 0, 0);  font-style: normal;  font-weight: 500;  font-stretch: normal;  font-family: adobe-courier;  font-size: 11pt;  text-decoration: none; }
span.default   { background: rgb(255, 255, 255);  color: rgb(0, 0, 0);  font-style: normal;  font-weight: 500;  font-stretch: normal;  font-family: adobe-courier;  font-size: 11pt;  text-decoration: none; }
span.default a { background: rgb(255, 255, 255);  color: rgb(0, 0, 0);  font-style: normal;  font-weight: 500;  font-stretch: normal;  font-family: adobe-courier;  font-size: 11pt;  text-decoration: underline; }
span.string   { color: rgb(188, 143, 143);  background: rgb(255, 255, 255);  font-style: normal;  font-weight: 500;  font-stretch: normal;  font-family: adobe-courier;  font-size: 11pt;  text-decoration: none; }
span.string a { color: rgb(188, 143, 143);  background: rgb(255, 255, 255);  font-style: normal;  font-weight: 500;  font-stretch: normal;  font-family: adobe-courier;  font-size: 11pt;  text-decoration: underline; }
span.comment   { color: rgb(178, 34, 34);  background: rgb(255, 255, 255);  font-style: normal;  font-weight: 500;  font-stretch: normal;  font-family: adobe-courier;  font-size: 11pt;  text-decoration: none; }
span.comment a { color: rgb(178, 34, 34);  background: rgb(255, 255, 255);  font-style: normal;  font-weight: 500;  font-stretch: normal;  font-family: adobe-courier;  font-size: 11pt;  text-decoration: underline; }
 --></style>

 </head>
  <body>

<pre>
      SUBROUTINE <a name="CHPGVD.1"></a><a href="chpgvd.f.html#CHPGVD.1">CHPGVD</a>( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
     $                   LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK driver routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          JOBZ, UPLO
      INTEGER            INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            IWORK( * )
      REAL               RWORK( * ), W( * )
      COMPLEX            AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="CHPGVD.21"></a><a href="chpgvd.f.html#CHPGVD.1">CHPGVD</a> computes all the eigenvalues and, optionally, the eigenvectors
</span><span class="comment">*</span><span class="comment">  of a complex generalized Hermitian-definite eigenproblem, of the form
</span><span class="comment">*</span><span class="comment">  A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A and
</span><span class="comment">*</span><span class="comment">  B are assumed to be Hermitian, stored in packed format, and B is also
</span><span class="comment">*</span><span class="comment">  positive definite.
</span><span class="comment">*</span><span class="comment">  If eigenvectors are desired, it uses a divide and conquer algorithm.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The divide and conquer algorithm makes very mild assumptions about
</span><span class="comment">*</span><span class="comment">  floating point arithmetic. It will work on machines with a guard
</span><span class="comment">*</span><span class="comment">  digit in add/subtract, or on those binary machines without guard
</span><span class="comment">*</span><span class="comment">  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
</span><span class="comment">*</span><span class="comment">  Cray-2. It could conceivably fail on hexadecimal or decimal machines
</span><span class="comment">*</span><span class="comment">  without guard digits, but we know of none.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  ITYPE   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          Specifies the problem type to be solved:
</span><span class="comment">*</span><span class="comment">          = 1:  A*x = (lambda)*B*x
</span><span class="comment">*</span><span class="comment">          = 2:  A*B*x = (lambda)*x
</span><span class="comment">*</span><span class="comment">          = 3:  B*A*x = (lambda)*x
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  JOBZ    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N':  Compute eigenvalues only;
</span><span class="comment">*</span><span class="comment">          = 'V':  Compute eigenvalues and eigenvectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  UPLO    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'U':  Upper triangles of A and B are stored;
</span><span class="comment">*</span><span class="comment">          = 'L':  Lower triangles of A and B are stored.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrices A and B.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AP      (input/output) COMPLEX array, dimension (N*(N+1)/2)
</span><span class="comment">*</span><span class="comment">          On entry, the upper or lower triangle of the Hermitian matrix
</span><span class="comment">*</span><span class="comment">          A, packed columnwise in a linear array.  The j-th column of A
</span><span class="comment">*</span><span class="comment">          is stored in the array AP as follows:
</span><span class="comment">*</span><span class="comment">          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1&lt;=i&lt;=j;
</span><span class="comment">*</span><span class="comment">          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j&lt;=i&lt;=n.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          On exit, the contents of AP are destroyed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  BP      (input/output) COMPLEX array, dimension (N*(N+1)/2)
</span><span class="comment">*</span><span class="comment">          On entry, the upper or lower triangle of the Hermitian matrix
</span><span class="comment">*</span><span class="comment">          B, packed columnwise in a linear array.  The j-th column of B
</span><span class="comment">*</span><span class="comment">          is stored in the array BP as follows:
</span><span class="comment">*</span><span class="comment">          if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1&lt;=i&lt;=j;
</span><span class="comment">*</span><span class="comment">          if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j&lt;=i&lt;=n.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          On exit, the triangular factor U or L from the Cholesky
</span><span class="comment">*</span><span class="comment">          factorization B = U**H*U or B = L*L**H, in the same storage
</span><span class="comment">*</span><span class="comment">          format as B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  W       (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">          If INFO = 0, the eigenvalues in ascending order.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Z       (output) COMPLEX array, dimension (LDZ, N)
</span><span class="comment">*</span><span class="comment">          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
</span><span class="comment">*</span><span class="comment">          eigenvectors.  The eigenvectors are normalized as follows:
</span><span class="comment">*</span><span class="comment">          if ITYPE = 1 or 2, Z**H*B*Z = I;
</span><span class="comment">*</span><span class="comment">          if ITYPE = 3, Z**H*inv(B)*Z = I.
</span><span class="comment">*</span><span class="comment">          If JOBZ = 'N', then Z is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDZ     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array Z.  LDZ &gt;= 1, and if
</span><span class="comment">*</span><span class="comment">          JOBZ = 'V', LDZ &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) COMPLEX array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, WORK(1) returns the required LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LWORK   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The dimension of array WORK.
</span><span class="comment">*</span><span class="comment">          If N &lt;= 1,               LWORK &gt;= 1.
</span><span class="comment">*</span><span class="comment">          If JOBZ = 'N' and N &gt; 1, LWORK &gt;= N.
</span><span class="comment">*</span><span class="comment">          If JOBZ = 'V' and N &gt; 1, LWORK &gt;= 2*N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment">          only calculates the required sizes of the WORK, RWORK and
</span><span class="comment">*</span><span class="comment">          IWORK arrays, returns these values as the first entries of
</span><span class="comment">*</span><span class="comment">          the WORK, RWORK and IWORK arrays, and no error message
</span><span class="comment">*</span><span class="comment">          related to LWORK or LRWORK or LIWORK is issued by <a name="XERBLA.102"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RWORK   (workspace) REAL array, dimension (MAX(1,LRWORK))
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LRWORK  (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The dimension of array RWORK.
</span><span class="comment">*</span><span class="comment">          If N &lt;= 1,               LRWORK &gt;= 1.
</span><span class="comment">*</span><span class="comment">          If JOBZ = 'N' and N &gt; 1, LRWORK &gt;= N.
</span><span class="comment">*</span><span class="comment">          If JOBZ = 'V' and N &gt; 1, LRWORK &gt;= 1 + 5*N + 2*N**2.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          If LRWORK = -1, then a workspace query is assumed; the
</span><span class="comment">*</span><span class="comment">          routine only calculates the required sizes of the WORK, RWORK
</span><span class="comment">*</span><span class="comment">          and IWORK arrays, returns these values as the first entries
</span><span class="comment">*</span><span class="comment">          of the WORK, RWORK and IWORK arrays, and no error message
</span><span class="comment">*</span><span class="comment">          related to LWORK or LRWORK or LIWORK is issued by <a name="XERBLA.117"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LIWORK  (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The dimension of array IWORK.
</span><span class="comment">*</span><span class="comment">          If JOBZ  = 'N' or N &lt;= 1, LIWORK &gt;= 1.
</span><span class="comment">*</span><span class="comment">          If JOBZ  = 'V' and N &gt; 1, LIWORK &gt;= 3 + 5*N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          If LIWORK = -1, then a workspace query is assumed; the
</span><span class="comment">*</span><span class="comment">          routine only calculates the required sizes of the WORK, RWORK
</span><span class="comment">*</span><span class="comment">          and IWORK arrays, returns these values as the first entries
</span><span class="comment">*</span><span class="comment">          of the WORK, RWORK and IWORK arrays, and no error message
</span><span class="comment">*</span><span class="comment">          related to LWORK or LRWORK or LIWORK is issued by <a name="XERBLA.131"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">          &gt; 0:  <a name="CPPTRF.136"></a><a href="cpptrf.f.html#CPPTRF.1">CPPTRF</a> or <a name="CHPEVD.136"></a><a href="chpevd.f.html#CHPEVD.1">CHPEVD</a> returned an error code:
</span><span class="comment">*</span><span class="comment">             &lt;= N:  if INFO = i, <a name="CHPEVD.137"></a><a href="chpevd.f.html#CHPEVD.1">CHPEVD</a> failed to converge;
</span><span class="comment">*</span><span class="comment">                    i off-diagonal elements of an intermediate
</span><span class="comment">*</span><span class="comment">                    tridiagonal form did not convergeto zero;
</span><span class="comment">*</span><span class="comment">             &gt; N:   if INFO = N + i, for 1 &lt;= i &lt;= n, then the leading
</span><span class="comment">*</span><span class="comment">                    minor of order i of B is not positive definite.
</span><span class="comment">*</span><span class="comment">                    The factorization of B could not be completed and
</span><span class="comment">*</span><span class="comment">                    no eigenvalues or eigenvectors were computed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Based on contributions by
</span><span class="comment">*</span><span class="comment">     Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            LQUERY, UPPER, WANTZ
      CHARACTER          TRANS
      INTEGER            J, LIWMIN, LRWMIN, LWMIN, NEIG
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.159"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.160"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="CHPEVD.163"></a><a href="chpevd.f.html#CHPEVD.1">CHPEVD</a>, <a name="CHPGST.163"></a><a href="chpgst.f.html#CHPGST.1">CHPGST</a>, <a name="CPPTRF.163"></a><a href="cpptrf.f.html#CPPTRF.1">CPPTRF</a>, CTPMV, CTPSV, <a name="XERBLA.163"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX, REAL
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      WANTZ = <a name="LSAME.172"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBZ, <span class="string">'V'</span> )
      UPPER = <a name="LSAME.173"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
<span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
         INFO = -1
      ELSE IF( .NOT.( WANTZ .OR. <a name="LSAME.179"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBZ, <span class="string">'N'</span> ) ) ) THEN
         INFO = -2
      ELSE IF( .NOT.( UPPER .OR. <a name="LSAME.181"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) ) THEN
         INFO = -3
      ELSE IF( N.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
         INFO = -9
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.EQ.0 ) THEN
         IF( N.LE.1 ) THEN
            LWMIN = 1
            LIWMIN = 1
            LRWMIN = 1
         ELSE
            IF( WANTZ ) THEN
               LWMIN = 2*N
               LRWMIN = 1 + 5*N + 2*N**2
               LIWMIN = 3 + 5*N
            ELSE
               LWMIN = N
               LRWMIN = N
               LIWMIN = 1
            END IF
         END IF
         WORK( 1 ) = LWMIN
         RWORK( 1 ) = LRWMIN
         IWORK( 1 ) = LIWMIN
<span class="comment">*</span><span class="comment">
</span>         IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
            INFO = -11
         ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
            INFO = -13
         ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
            INFO = -15
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.219"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CHPGVD.219"></a><a href="chpgvd.f.html#CHPGVD.1">CHPGVD</a>'</span>, -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Form a Cholesky factorization of B.
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="CPPTRF.232"></a><a href="cpptrf.f.html#CPPTRF.1">CPPTRF</a>( UPLO, N, BP, INFO )
      IF( INFO.NE.0 ) THEN
         INFO = N + INFO
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Transform problem to standard eigenvalue problem and solve.
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="CHPGST.240"></a><a href="chpgst.f.html#CHPGST.1">CHPGST</a>( ITYPE, UPLO, N, AP, BP, INFO )
      CALL <a name="CHPEVD.241"></a><a href="chpevd.f.html#CHPEVD.1">CHPEVD</a>( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
     $             LRWORK, IWORK, LIWORK, INFO )
      LWMIN = MAX( REAL( LWMIN ), REAL( WORK( 1 ) ) )
      LRWMIN = MAX( REAL( LRWMIN ), REAL( RWORK( 1 ) ) )
      LIWMIN = MAX( REAL( LIWMIN ), REAL( IWORK( 1 ) ) )
<span class="comment">*</span><span class="comment">
</span>      IF( WANTZ ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Backtransform eigenvectors to the original problem.
</span><span class="comment">*</span><span class="comment">
</span>         NEIG = N
         IF( INFO.GT.0 )
     $      NEIG = INFO - 1
         IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
</span><span class="comment">*</span><span class="comment">           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
</span><span class="comment">*</span><span class="comment">
</span>            IF( UPPER ) THEN
               TRANS = <span class="string">'N'</span>
            ELSE
               TRANS = <span class="string">'C'</span>
            END IF
<span class="comment">*</span><span class="comment">
</span>            DO 10 J = 1, NEIG
               CALL CTPSV( UPLO, TRANS, <span class="string">'Non-unit'</span>, N, BP, Z( 1, J ),
     $                     1 )
   10       CONTINUE
<span class="comment">*</span><span class="comment">
</span>         ELSE IF( ITYPE.EQ.3 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           For B*A*x=(lambda)*x;
</span><span class="comment">*</span><span class="comment">           backtransform eigenvectors: x = L*y or U'*y
</span><span class="comment">*</span><span class="comment">
</span>            IF( UPPER ) THEN
               TRANS = <span class="string">'C'</span>
            ELSE
               TRANS = <span class="string">'N'</span>
            END IF
<span class="comment">*</span><span class="comment">
</span>            DO 20 J = 1, NEIG
               CALL CTPMV( UPLO, TRANS, <span class="string">'Non-unit'</span>, N, BP, Z( 1, J ),
     $                     1 )
   20       CONTINUE
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      WORK( 1 ) = LWMIN
      RWORK( 1 ) = LRWMIN
      IWORK( 1 ) = LIWMIN
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="CHPGVD.293"></a><a href="chpgvd.f.html#CHPGVD.1">CHPGVD</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

</pre>

 </body>
</html>
